Lectures on Topological Dynamics
Author | : Robert Ellis |
Publisher | : New York : W. A. Benjamin |
Total Pages | : 0 |
Release | : 1969 |
Genre | : Dynamics |
ISBN | : 9780805324211 |
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Author | : Robert Ellis |
Publisher | : New York : W. A. Benjamin |
Total Pages | : 0 |
Release | : 1969 |
Genre | : Dynamics |
ISBN | : 9780805324211 |
Author | : Robert Ellis |
Publisher | : |
Total Pages | : 240 |
Release | : 1969 |
Genre | : Dynamics |
ISBN | : |
Author | : Mitchell A. Berger |
Publisher | : Springer Science & Business Media |
Total Pages | : 240 |
Release | : 2009-05-05 |
Genre | : Mathematics |
ISBN | : 3642008364 |
This volume contains a wide-ranging collection of valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics to DNA tangles and knotted DNAs in sedimentation.
Author | : Ya. B. Pesin |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821848895 |
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.
Author | : Lawrence Markus |
Publisher | : American Mathematical Soc. |
Total Pages | : 85 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : 0821816950 |
Offers an exposition of the central results of Differentiable Dynamics. This edition includes an Appendix reviewing the developments under five basic areas: nonlinear oscillations, diffeomorphisms and foliations, general theory; dissipative dynamics, general theory; conservative dynamics, and, chaos, catastrophe, and multi-valued trajectories.
Author | : Valentin Senderovich Afraĭmovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 367 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821831682 |
Basic concepts Zero-dimensional dynamics One-dimensional dynamics Two-dimensional dynamics Systems with 1.5 degrees of freedom Systems generated by three-dimensional vector fields Lyapunov exponents Appendix Bibliography Index.
Author | : Mitchell A. Berger |
Publisher | : Springer |
Total Pages | : 240 |
Release | : 2009-05-28 |
Genre | : Science |
ISBN | : 3642008372 |
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.
Author | : Paul R. Halmos |
Publisher | : Courier Dover Publications |
Total Pages | : 113 |
Release | : 2017-11-15 |
Genre | : Mathematics |
ISBN | : 0486826848 |
This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.
Author | : George R. Sell |
Publisher | : |
Total Pages | : |
Release | : 1967 |
Genre | : |
ISBN | : |
Author | : Benjamin Weiss |
Publisher | : American Mathematical Soc. |
Total Pages | : 127 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821804146 |
This book presents the expanded notes from ten lectures given by the author at the NSF/CBMS conference held at California State University (Bakersfield). The author describes what he calls single orbit dynamics, which is an approach to the analysis of dynamical systems via the study of single orbits, rather than the study of a system as a whole. He presents single orbit interpretations of several areas of topological dynamics and ergodic theory and some new applications of dynamics to graph theory. In the concluding lectures, single orbit approaches to generalizations of the Shannon-Breiman-McMillan theorem and related problems of compression and universal coding are presented. Complete proofs and illuminating discussions are included and references for further study are given. Some of the material appears here for the first time in print.